I don’t think wondering what someone’s mental health/upbringing is/was like is being sympathetic towards them when that person has gone to commit a terrible horrendous crime(s). I have poor mental health myself and had a shifty upbringing, for what it’s worth. I am not a child abuser but I’m not offended by people pondering this.
This.
Just as with physical disability - e.g. Stevie Wonder can travel around, walk, talk, sing, play an instrument etc whereas Stephen Hawking couldn't, but could understand complex scientific concepts far better than almost anybody else (including probably Stevie); but both are/were significantly disabled - there's a wide spectrum of mental illness.
Just because it manifests in one person in one way, that doesn't mean it will affect another person in anything like the same manner.
It can be a contributory and explanatory factor, but is by no means an excuse, when somebody goes from their own individual 'starting point' but then makes terrible decisions from then on.
If a millionaire and a pauper both steal food from a shop, they've both deliberately committed the same, equally-bad crime - but you can much more easily see what may have led the latter to make that conscious decision to do wrong than the former.